Simsimd

-------------------------------------------------------------------------------------------------------------
Benchmark Time CPU Iterations UserCounters...
-------------------------------------------------------------------------------------------------------------
fma_f64_haswell<1536d>/min_time:10.000/threads:1 1344 ns 1344 ns 10391897 abs_delta=0 bytes=27.4208G/s pairs=743.836k/s relative_error=0
wsum_f64_haswell<1536d>/min_time:10.000/threads:1 1040 ns 1040 ns 13465261 abs_delta=0 bytes=23.6376G/s pairs=961.815k/s relative_error=0
fma_f32_haswell<1536d>/min_time:10.000/threads:1 651 ns 651 ns 21534450 abs_delta=23.597n bytes=28.3033G/s pairs=1.53555M/s relative_error=47.0002n
wsum_f32_haswell<1536d>/min_time:10.000/threads:1 392 ns 392 ns 36225731 abs_delta=19.6436n bytes=31.3326G/s pairs=2.54985M/s relative_error=54.2672n
fma_f16_haswell<1536d>/min_time:10.000/threads:1 188 ns 188 ns 74334715 abs_delta=9.24044u bytes=49.1302G/s pairs=5.33097M/s relative_error=18.3975u
wsum_f16_haswell<1536d>/min_time:10.000/threads:1 130 ns 129 ns 106997523 abs_delta=12.015u bytes=47.4441G/s pairs=7.72203M/s relative_error=33.1896u
fma_bf16_haswell<1536d>/min_time:10.000/threads:1 225 ns 225 ns 62443286 abs_delta=1.91338m bytes=41.0221G/s pairs=4.45118M/s relative_error=3.81108m
wsum_bf16_haswell<1536d>/min_time:10.000/threads:1 161 ns 161 ns 86471812 abs_delta=1.36093m bytes=38.1318G/s pairs=6.20635M/s relative_error=3.75961m
fma_u8_sapphire<1536d>/min_time:10.000/threads:1 70.9 ns 70.9 ns 197232316 abs_delta=9.2812 bytes=64.9867G/s pairs=14.103M/s relative_error=2.45142m
wsum_u8_sapphire<1536d>/min_time:10.000/threads:1 50.6 ns 50.6 ns 276672248 abs_delta=8.89144 bytes=60.6775G/s pairs=19.7518M/s relative_error=3.28203m
fma_i8_sapphire<1536d>/min_time:10.000/threads:1 94.0 ns 94.0 ns 149003863 abs_delta=10.1192 bytes=49.0403G/s pairs=10.6424M/s relative_error=6.98359m
wsum_i8_sapphire<1536d>/min_time:10.000/threads:1 70.4 ns 70.4 ns 198873173 abs_delta=9.76862 bytes=43.613G/s pairs=14.197M/s relative_error=9.3472m
fma_f64_skylake<1536d>/min_time:10.000/threads:1 1340 ns 1340 ns 10460553 abs_delta=39.3003a bytes=27.5182G/s pairs=746.479k/s relative_error=78.2836a
wsum_f64_skylake<1536d>/min_time:10.000/threads:1 1036 ns 1036 ns 13484768 abs_delta=28.4608a bytes=23.717G/s pairs=965.047k/s relative_error=78.6298a
fma_f32_skylake<1536d>/min_time:10.000/threads:1 626 ns 626 ns 22261554 abs_delta=25.3818n bytes=29.4286G/s pairs=1.5966M/s relative_error=50.5553n
wsum_f32_skylake<1536d>/min_time:10.000/threads:1 386 ns 386 ns 35032887 abs_delta=19.7444n bytes=31.8146G/s pairs=2.58908M/s relative_error=54.5454n
fma_bf16_skylake<1536d>/min_time:10.000/threads:1 188 ns 188 ns 74667249 abs_delta=415.805u bytes=48.9511G/s pairs=5.31154M/s relative_error=827.962u
wsum_bf16_skylake<1536d>/min_time:10.000/threads:1 147 ns 147 ns 95128759 abs_delta=269.793u bytes=41.8834G/s pairs=6.81696M/s relative_error=745.331u
fma_f16_serial<1536d>/min_time:10.000/threads:1 900 ns 900 ns 15592180 abs_delta=2.97965u bytes=10.2444G/s pairs=1.11159M/s relative_error=5.93995u
wsum_f16_serial<1536d>/min_time:10.000/threads:1 821 ns 821 ns 17058449 abs_delta=1.11521u bytes=7.48594G/s pairs=1.21841M/s relative_error=3.07961u
fma_u8_serial<1536d>/min_time:10.000/threads:1 6692 ns 6692 ns 2089290 abs_delta=1.66854 bytes=688.583M/s pairs=149.432k/s relative_error=440.882u
wsum_u8_serial<1536d>/min_time:10.000/threads:1 5577 ns 5577 ns 2508971 abs_delta=2.32787 bytes=550.797M/s pairs=179.296k/s relative_error=859.403u
fma_i8_serial<1536d>/min_time:10.000/threads:1 6874 ns 6874 ns 2039761 abs_delta=5.14013 bytes=670.367M/s pairs=145.479k/s relative_error=3.54862m
wsum_i8_serial<1536d>/min_time:10.000/threads:1 5851 ns 5851 ns 2394538 abs_delta=6.36953 bytes=525.018M/s pairs=170.904k/s relative_error=6.09231m

| `avx512_f32_js_1536d` | 1.127 M/s | 13.84 G/s | 0.001 | 345u |
| `avx512_f16_js_1536d` | 2.139 M/s | 13.14 G/s | 0.070 | 0.020 |
| `avx2_f16_js_1536d` | 0.547 M/s | 3.36 G/s | 0.011 | 0.003 |

Of course, the results will vary depending on the vector size. I generally use 1536 dimensions, matching the size of OpenAI Ada embeddings, standard in NLP workloads. The Jensen Shannon divergence, however, is used broadly in other domains of statistics, bio-informatics, and chem-informatics, so I'm adding it as a new out-of-the-box supported metric into [USearch](https://github.com/unum-cloud/usearch) today 🥳

This further accelerates the k-approximate Nearest Neighbors Search and the [clustering of Billions of different protein sequences](https://github.com/unum-cloud/usearch#clustering) without alignment procedures. [Expect one more "Less Slow" post soon!](https://ashvardanian.com/tags/less-slow/) 🤗